Second Law Analysis of a Carbon Dioxide Transcritical Power System in Low-grade Heat Source Recovery
Y. Chen , Almaz Bitew Workie , Per Lundqvist
Div. of Applied Thermodynamics and Refrigeration, Department of Energy Technology, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Abstract Employing Carbon dioxide as a working media in power cycles for low-grade heat source utilization has attracted more and more attentions. However, compared to other well-known cycles that employed in low-grade heat source utilizations, the information about CO2 power cycle is still very limited. In the current work, the performance of a CO2 power cycle in utilizing the low-grade heat sources is simulated and the results are analyzed with a focus on second law thermodynamics (i.e. exergy and entropy). Different system parameters that influencing the system exergy and entropy change are discussed.
Engineering Equation Solver (EES) is used for simulation. The simulation results show that the matching of the temperature profiles in the system heat exchangers has crucial influences on their exergy destructions and entropy generations. It is also an essential factor that influences the system thermodynamic efficiencies.
Keywords: Carbon dioxide, exergy analysis, transcritical cycle, high pressure pump
Nomenclature
EES Engineer Equation Solver C Contribution of entropy generation % Cp Specific heat kJ/kg K GWP Global Warming Potential m Mass flow rate kg s-1 ODP Ozone Depleting Potential ORC Organic Rankine Cycle Q Energy kW SC CO2 Supercritical carbon dioxide Wexp Work from the expansion process kW Wnet Net work from the SC CO2 cycle kW Wp Work supply to the Pump kW
Greek alphabet symbols ηexg Exergy efficiency ηth Thermal efficiency Specific exergy kJ/kg Exergy kW φ Entropy generation kJ/kg K
Corresponding author. Tel.: +46-(0)8-790-7435 Fax: +46-8-203-007 E-mail address: [email protected] (Y. Chen) Subscripts a average a − g Cycle working route points c Condenser exp Expander h-h’ Cooling media condition point gas Heat source gh Gas heater gc Gas cooling in Heat exchanger inlet is Isentropic out Heat exchanger outlet m Mechanical p Pump T Turbine th Thermal w Water
Introduction Energy security, economic development and environment protection are not well balanced today and the energy demand is still closely connected to the economic growth. Among the energy resources worldwide, fossil fuels still play the dominant role, which account for 77% of the increasing energy demand 2007-2030 [ 1 ] . Consequently, the dramatic increase of the energy demand due to the worldwide economic growth has caused more and more severe environmental problems, as air pollution, climate changes etc. The predicted energy related CO2 emission will rise 130% by year 2050 and can result in a global temperature increase by 6 °C [ 2 ] .
Improving the energy efficiency by utilizing the energy in low-grade heat source / surplus heat offers a great opportunity for a sustainable energy future and less environmental problems. Figure 1 shows the typical temperature range of different renewable/ surplus heat sources. The heat sources with available temperature lower than 300 °C are normally considered as low-grade heat sources, for which conventional steam Rankin cycle is not proper for heat recovery, due to its low thermal efficiency, large volume flow and erosion of the turbine blades [ 3 ] .
Figure 1 typical temperature range of different heat sources for heat recovery1
1 Pictures are from internet and only for symbolizing different heat sources The research on low-grade heat source utilization with power cycles that utilizing CO2 as a working fluid has caused more and more attentions in recent years. This is not only due to the reason that CO2 is environmental benign, low-cost, non-toxic and non-flammable, but also because the supercritical CO2 temperature profile can provide a better match to the low-grade heat source temperature profile than other working fluids that used in conventional cycles. This will help CO2 system to reduce the irreversibility in its heating process, which gives a better thermal efficiency than the systems with conventional working fluids.
Among the research on CO2 power cycles in low-grade heat source utilization, Zhang and his colleagues investigated the potential of CO2 power cycle in utilizing the solar energy both theoretically and experimentally [ 4 ] -[ 8 ] . Chen et al. investigated the performance of a carbon dioxide power cycle in utilizing the low-grade heat sources and compared its performance with Organic Rankine Cycles (ORC) [ 9 ] - [ 11 ] . Moreover, Cayer and his colleagues studied CO2 power system under fixed system working conditions and discussed system optimizations [ 12 ] . Wang et al. tried to optimize the working parameters of supercritical CO2 power cycle under a fixed heat source condition by using genetic algorithm and artificial neural network with an assumption that the system heat exchangers will provide sufficient heating /cooling to the desired cycle working conditions [ 13 ] .
In the current study, the performance of a carbon dioxide transcritical power system is simulated with a given heat source condition. The system’s performance is analyzed from a second law thermodynamic viewpoint (exergy and entropy) with a focus on the matching of the temperature profiles in the system heat exchangers and its influence on the system performance. Engineering Equation Solver (EES) is employed for the simulation.
System description
A basic CO2 transcritical power system consists of four main components, namely a pump, a gas heater, an expansion device and a condenser. The system schematic layout and the corresponding T-S chart are shown in Figure 2.
Figure 2 Schematic layout and the corresponding T-S chart of a CO2 transcritical power system
As illustrated in the schematic T-S chart (Figure 2) that CO2 still holds a high temperature at the expansion outlet (point 13), and its energy can be further recovered to produce warm water for space heating (e.g. floor heating). To be able to recover this energy sufficiently and to avoid the pinching2
2 Pinching is the minimum temperature difference inside a heat exchanger , which limited the heat exchanger performance (due to the phase changing of CO2) in its condensing process, the condenser can be divided into two heat exchangers, namely condenser and gas cooler. Condenser will be used to condense the CO2 from its saturated phase to the liquid phase, before it enters the pump (point 22 to point 1). The gas cooler will be used to recover the energy from expansion outlet CO2 to produce warm water (point 13 to point 22) for space heating.
Simulation conditions description
The following general assumptions are made for the thermodynamic analysis of the cycle:
‐ The heat source is assumed to have an available temperature of 160 o C and a mass flow rate of 10kg/s
‐ The cycle is considered to work at steady state
‐ Pressure drops in the heat exchangers are neglected
‐ Isentropic efficiencies of the pump and the expansion machine are assumed to be 0.85 and 0.8 respectively and the mechanical efficiency is assumed to be 0.95 for both
‐ The pinching in the condenser is assumed to be 5 o C
‐ The condensing pressure is assumed to be 60 bar
‐ The cooling water inlet temperature is assumed to be 15 o C
‐ The set value for the water outlet temperature from the gas cooler is 50 o C
Following equations are used in the simulation model.
The heat balance of the gas heater (process 2 to 11) can be expressed as:
Q m Cp t t Equation 1
Q m CO h h Equation 2
The power consumption of the pump is calculated by the following equation: